Hydrodynamics of bubble flow through a porous medium with applications to packed bed reactors

TL;DR

This paper addresses the challenge of predicting bubble dynamics in gas–liquid flow through packed-bed reactors (PBRs), particularly under microgravity. It introduces time-dependent, pore-scale dynamic scales based on the interfacial area $A_ ext{int}$ and defines inertia–capillarity–buoyancy balances through $F_I$, $F_C$, and $F_B$, yielding modified Weber and Bond numbers $We^*$ and $Bo^*$ and the key ratio $We^*/(1+Bo^*)$ to distinguish bubble displacement from entrapment. Using 3D volume-of-fluid (VOF) CFD on a representative-element volume, the study demonstrates microgravity bubble regimes, including capillary entrapment, inertia-driven displacement, and bubble breakup, as well as gravity-modulated transitions to buoyancy entrapment. The results provide a physically grounded framework for predicting pore-scale regime transitions and motivate development of reduced-order models for pulse formation in PBRs, with implications for space-based and terrestrial reactor design and operation.

Abstract

Gas-liquid flows through packed bed reactors (PBRs) are challenging to predict due to the tortuous flow paths that fluid interfaces must traverse. Experiments at the International Space Station showed that bubble and pulse flows are predominately observed under microgravity conditions, while the trickle and spray flows observed under terrestrial conditions are not present in microgravity. To understand the physics behind the former experiments, we simulate bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrate different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we perform a quantitative analysis by introducing new dynamic scales, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis leads us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement.

Figures (9)

• Figure 1: Comparison of the radial porosity variation of the 3D PBR geometry generated for this study and the correlation of de Klerk DeKlerk_Val.
• Figure 2: PBR representative element volume (REV) generated for the CFD simulations, comprising of a $3~mm$ diameter sphere packing within a cylindrical column of $12~mm$ height and $12~mm$ diameter. Note that the darker regions in the figure represent the spherical packing.
• Figure 3: Surface and volume mesh of the PBR REV generated using the fault-tolerant meshing workflow with the parameters in Table \ref{['tab::mesh_param']}.
• Figure 4: Schematic representation of the REV geometry and boundary conditions on it used in the CFD simulations of the dynamics of bubble flow through a PBR.
• Figure 5: Bubble evolution Bubble evolution in 2D axial profiles (top and middle rows) and 3D isometric views (bottom rows) for (a) $We_{d_p} = 0.165$ showing capillary entrapment and (b) $We_{d_p} = 1.0$ showing inertia-induced bubble displacement. Note the liquid flow is in the $+z$ direction.